P4.4: Quadratic Formula and the Discriminant

Last updated almost 4 years ago

14 questions

Note from the author:

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

Instructions

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

P4.4: Quadratic Formula and the Discriminant

Last updated almost 4 years ago

14 questions

Note from the author:

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

Instructions

Watch this video for solving with the quadratic formula.
Watch this video for a review of using the discriminant.

Match the discriminant with the indicated type of roots.

This won't turn green until you have them ALL right.

Draggable item		Corresponding Item
discriminant is a positive perfect square		2 real rational roots
discriminant is positive, but not a perfect square		2 real irrational roots
discriminant is 0		1 unique root
discriminant is negative		2 nonreal roots

Find the discriminant of

x2+12x-8 = 0

Enter your answer as a number, no spaces.

Solve

x2+12x-8=0.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of
13x^{2}-16x=x^{2}-x

Enter your answer as a number, no spaces.

Solve
13x^{2}-16x = x^{2}-x.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of

8x^{2}+15x = 7x-4

Enter your answer as a number, no spaces.

Solve
8x^{2}+15x = 7x-4

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

This one will be "ugly".

Find the discriminant of
5x^{2}+1 = 4x -7

Enter your answer as a number, no spaces.

Solve
5x^{2}+1 = 4x-7

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of
-2x^{2}+24 = 8x

Enter your answer as a number, no spaces.

Solve
-2x^{2}+24 = 8x

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is 122. Which describes the number and type of roots for that equation?

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?

Hint: Check this with #1!

REVIEW
Solve by square roots.

2(x+1)^{2}+5 = -3

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.
If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

P4.4: Quadratic Formula and the Discriminant

P4.4: Quadratic Formula and the Discriminant

Match the discriminant with the indicated type of roots.This won't turn green until you have them ALL right.

Find the discriminant of x2+12x-8 = 0Enter your answer as a number, no spaces.

Solve x2+12x-8=0.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of13x^{2}-16x=x^{2}-xEnter your answer as a number, no spaces.

Solve13x^{2}-16x = x^{2}-x.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of8x^{2}+15x = 7x-4Enter your answer as a number, no spaces.

Solve8x^{2}+15x = 7x-4Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.This one will be "ugly".

Find the discriminant of5x^{2}+1 = 4x -7Enter your answer as a number, no spaces.

Solve5x^{2}+1 = 4x-7Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of-2x^{2}+24 = 8xEnter your answer as a number, no spaces.

Solve-2x^{2}+24 = 8xEnter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is 122. Which describes the number and type of roots for that equation?

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?Hint: Check this with #1!

REVIEW Solve by square roots.2(x+1)^{2}+5 = -3Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Match the discriminant with the indicated type of roots.This won't turn green until you have them ALL right.

Find the discriminant of x2+12x-8 = 0Enter your answer as a number, no spaces.

Solve x2+12x-8=0.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of13x^{2}-16x=x^{2}-xEnter your answer as a number, no spaces.

Solve13x^{2}-16x = x^{2}-x.Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of8x^{2}+15x = 7x-4Enter your answer as a number, no spaces.

Solve8x^{2}+15x = 7x-4Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.This one will be "ugly".

Find the discriminant of5x^{2}+1 = 4x -7Enter your answer as a number, no spaces.

Solve5x^{2}+1 = 4x-7Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of-2x^{2}+24 = 8xEnter your answer as a number, no spaces.

Solve-2x^{2}+24 = 8xEnter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is 122. Which describes the number and type of roots for that equation?

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?Hint: Check this with #1!

REVIEW Solve by square roots.2(x+1)^{2}+5 = -3Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Match the discriminant with the indicated type of roots.

This won't turn green until you have them ALL right.

Find the discriminant of

x2+12x-8 = 0

Enter your answer as a number, no spaces.

Solve

x2+12x-8=0.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of
13x^{2}-16x=x^{2}-x

Enter your answer as a number, no spaces.

Solve
13x^{2}-16x = x^{2}-x.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of

8x^{2}+15x = 7x-4

Enter your answer as a number, no spaces.

Solve
8x^{2}+15x = 7x-4

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

This one will be "ugly".

Find the discriminant of
5x^{2}+1 = 4x -7

Enter your answer as a number, no spaces.

Solve
5x^{2}+1 = 4x-7

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of
-2x^{2}+24 = 8x

Enter your answer as a number, no spaces.

Solve
-2x^{2}+24 = 8x

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?

Hint: Check this with #1!

REVIEW
Solve by square roots.

2(x+1)^{2}+5 = -3

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.
If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Match the discriminant with the indicated type of roots.

This won't turn green until you have them ALL right.

Find the discriminant of

x2+12x-8 = 0

Enter your answer as a number, no spaces.

Solve

x2+12x-8=0.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

Find the discriminant of
13x^{2}-16x=x^{2}-x

Enter your answer as a number, no spaces.

Solve
13x^{2}-16x = x^{2}-x.

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals. No decimals.

Find the discriminant of

8x^{2}+15x = 7x-4

Enter your answer as a number, no spaces.

Solve
8x^{2}+15x = 7x-4

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

This one will be "ugly".

Find the discriminant of
5x^{2}+1 = 4x -7

Enter your answer as a number, no spaces.

Solve
5x^{2}+1 = 4x-7

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

Find the discriminant of
-2x^{2}+24 = 8x

Enter your answer as a number, no spaces.

Solve
-2x^{2}+24 = 8x

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.

If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.

The discriminant of a quadratic equation is -36. Which describes the number and type of roots for that equation?

Hint: Check this with #1!

REVIEW
Solve by square roots.

2(x+1)^{2}+5 = -3

Enter your answer as x={#, #}, with only 1 space after the comma, with the smaller number entered first. Simplify all fractions and radicals.
If your #s are imaginary numbers, enter them in the form a+bi, where a and b are real numbers.